CN112861317A - Kinematic modeling method for joint type coordinate measuring machine for compensating inclination error of rotating shaft - Google Patents

Kinematic modeling method for joint type coordinate measuring machine for compensating inclination error of rotating shaft Download PDF

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CN112861317A
CN112861317A CN202110034461.0A CN202110034461A CN112861317A CN 112861317 A CN112861317 A CN 112861317A CN 202110034461 A CN202110034461 A CN 202110034461A CN 112861317 A CN112861317 A CN 112861317A
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rotating shaft
measuring machine
coordinate measuring
articulated
error motion
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CN112861317B (en
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于连栋
曹家铭
赵会宁
李维诗
夏豪杰
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Hefei University of Technology
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
    • G01B21/02—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness
    • G01B21/04—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness by measuring coordinates of points
    • G01B21/042—Calibration or calibration artifacts

Abstract

The invention discloses a kinematic modeling method for an articulated coordinate measuring machine for compensating a tilt error of a rotating shaft, which comprises the following steps: s1, building a tilt error motion test system of the rotating shaft of the articulated coordinate measuring machine, and actually measuring the tilt error motion of each rotating shaft of the articulated coordinate measuring machine; s2, fitting the measurement result by utilizing Fourier series, and establishing a functional relation between the rotation angle of the rotating shaft and the inclination error motion so as to obtain a compensation formula of the inclination error of the rotating shaft; and S3, combining the compensation formula with the joint type coordinate measuring machine kinematic model, and then establishing the joint type coordinate measuring machine kinematic model containing the rotation axis inclination error motion. The model established by the invention can avoid the influence of the inclination error of the rotating shaft on the measurement precision, and greatly improve the measurement precision of the articulated coordinate measuring machine.

Description

Kinematic modeling method for joint type coordinate measuring machine for compensating inclination error of rotating shaft
Technical Field
The invention relates to the technical field of articulated coordinate measuring machines, in particular to a kinematic modeling method for an articulated coordinate measuring machine, which is used for compensating inclination errors of a rotating shaft.
Background
The articulated coordinate measuring machine is a high-precision geometric measuring instrument, has the advantages of light weight, good portability and high degree of freedom compared with the traditional orthogonal three-coordinate measuring machine, is widely applied to the fields of automobile manufacturing, aerospace, large part manufacturing and the like for on-site rapid measurement, and a kinematic model of the articulated coordinate measuring machine is an important guarantee for measuring precision.
Since the articulated coordinate measuring machine is similar in structure to an industrial robot, a robot kinematics modeling method is used for reference and improved in its kinematics modeling. The D-H model is the most classical modeling theory of the robot, but when the axes of adjacent joints are parallel to each other, the classical four-parameter D-H model cannot accurately describe the structural parameters between the adjacent joints, and the ill-conditioned nature exists. The technicians respectively provide an improved four-parameter DH model and an improved five-parameter D-H model on the basis of a D-H model to overcome the ill-condition when two adjacent joint axes are parallel or nearly parallel. There are other models in the field of robot modeling, such as the CPC (complete and parametric connectivity) model, the MCPC (modified CPC) model, the POE (product of exposure) model, the Local POE model, etc.
However, in the above-described kinematic model of the articulated coordinate measuring machine or robot, only the structure parameter error is considered, and the influence of the error motion of the rotation axis on the accuracy is not considered. Due to the serial structure of the articulated coordinate measuring machine or the robot, the inclination error movement of the rotating shaft has an amplification effect on the precision of the articulated coordinate measuring machine or the robot, and the position of the tail end of the articulated coordinate measuring machine or the robot can be obviously changed. As can be seen from simulation analysis, in an ideal state, a tilt error motion of the order of an angle second is added to the rotation axis, and the end probe causes a deviation of the order of millimeters. Therefore, the in-line measuring instrument or the industrial robot having the rotating shaft has the above problems.
In order to further improve the measurement accuracy of the articulated coordinate measuring machine, the applicant proposes a measurement model of the articulated coordinate measuring machine with rotation axis tilt error motion compensation.
Disclosure of Invention
The invention aims to provide a kinematic modeling method for an articulated coordinate measuring machine, which compensates a tilt error of a rotating shaft.
In order to achieve the purpose, the technical scheme of the invention is as follows: a kinematic modeling method for an articulated coordinate measuring machine that compensates for tilt errors of a rotating shaft, comprising the steps of:
s1, building a tilt error motion test system of the rotating shaft of the articulated coordinate measuring machine, and actually measuring the tilt error motion of each rotating shaft of the articulated coordinate measuring machine;
s2, fitting the measurement result by utilizing Fourier series, and establishing a functional relation between the rotation angle of the rotating shaft and the inclination error motion so as to obtain a compensation formula of the inclination error of the rotating shaft;
and S3, combining the compensation formula with the joint type coordinate measuring machine kinematic model, and then establishing the joint type coordinate measuring machine kinematic model containing the rotation axis inclination error motion.
Further, the calculation process of the compensation formula in S2 specifically includes:
establishment of epsilonxAnd εyIn a one-to-one mapping relationship
Figure BDA0002892906480000031
Using Fourier series to exiAnd εyiFitting to establish a functional relationship between the rotation angle of the rotating shaft and the tilt error motion
Figure BDA0002892906480000032
Wherein n is 7;
thereby obtaining the coordinate conversion relation of the rotating shaft
Figure BDA0002892906480000033
DiSatisfies the coordinate transformation formula T ═ Di·Treal，TrealIs a rotating shaft actual coordinate system, and T is a coordinate system after compensating the rotating shaft inclination error motion; because of ex、εyThe value is small, and a compensation formula can be obtained by simplifying the coordinate conversion relation
Figure BDA0002892906480000034
Further, the kinematic model of the articulated coordinate measuring machine including the tilt error motion of the rotation axis described in S3 is
Figure BDA0002892906480000041
Wherein A isiAnd representing a homogeneous coordinate transformation matrix to determine the relative pose between the adjacent rods.
The invention has the beneficial effects that: the modeling method comprises the steps of firstly carrying out actual measurement on the inclination error movement of each rotating shaft forming the articulated coordinate measuring machine, fitting the measurement result by utilizing Fourier series, establishing a functional relation between the rotation angle of the rotating shaft and the inclination error movement, and then obtaining a compensation formula capable of offsetting the inclination error of the rotating shaft through calculation, thereby establishing a kinematic model of the articulated coordinate measuring machine containing the inclination error movement of the rotating shaft, wherein the kinematic model can avoid the influence of the inclination error of the rotating shaft on the measurement precision, and greatly improve the measurement precision of the articulated coordinate measuring machine.
Drawings
FIG. 1 is a schematic view of a rotating shaft error analysis;
FIG. 2 is a flow chart of a method of kinematic modeling of an articulated coordinate measuring machine that compensates for rotational axis tilt errors;
fig. 3 is a measurement schematic diagram of a rotation axis inclination error motion measurement system.
Detailed Description
The technical solution in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.
Ideally, the axis of rotation has only one degree of freedom for rotation about the z-axis, and the other 5 degrees of freedom are constrained, i.e., there is no error motion in the axis of rotation. However, in practical situations, due to reasons such as machining, assembly, temperature variation and wear in use, there is a difference between the motion of the rotating shaft and the ideal state, and there are 6 error motions as shown in fig. 1, which are: axial error motion (delta)z) Radial error motion (delta)x，δy) Tilt error motion (epsilon)x、εy) Angular positioning error motion (epsilon)z)。
For tilt error motion (ε)x、εy) Compensating for tilt error motion of each axis of rotation by a rotation epsilon in the x and y directions, respectivelyxiAnd εyiThe effect of the tilt error motion can be counteracted.
Based on this, the present embodiment provides a method for modeling kinematics of an articulated coordinate measuring machine capable of compensating for a tilt error motion of a rotation axis, as shown in fig. 2, including the following steps:
s1, building a system for testing the inclination error movement of the rotating shaft of the articulated coordinate measuring machine, and actually measuring the inclination error movement of each rotating shaft of the articulated coordinate measuring machine to obtain the rotation angle theta of the rotating shaftiDependent variable epsilon changed by changexAnd εy。
With respect to tilt error motion (epsilon)xAnd εy) The measurement of (2):
the GJB1801-93 "main performance test method for inertia technology test equipment" has clearly specified measurement and error separation methods for tilt error motion of a rotating shaft, namely a level meter method and an autocollimator method, and the autocollimator is matched with a plane mirror to measure the tilt error motion of the rotating shaft.
The rotation axis inclination error motion measurement system is shown in fig. 3, the rotation axis and the auxiliary fixture are matched through threads, the plane mirror is fixed on the auxiliary fixture, the auxiliary fixture is adjusted to enable the light return cross target of the plane reflector to be located in the center of the view field of the autocollimator A as far as possible, and the cross targets are guaranteed to be located in the view field of the autocollimator A under the condition that the rotation spindle rotates for a circle.
Because each rotating shaft uses an incremental circular grating sensor, zero-crossing operation is required; in order to ensure the data processing effect and the accuracy and the repeatability of curve drawing, the measured rotating shaft is rotated according to a fixed rotating angle, and the reading theta of the circular grating sensor of the rotating shaft is recordediAnd the readout of autocollimator A in the x and y directions, i.e. the tilt error motion (. epsilon.)xAnd εy)。
And S2, fitting the measurement result by utilizing Fourier series, and establishing a functional relation between the rotation angle of the rotating shaft and the inclination error movement, thereby obtaining a compensation formula of the inclination error of the rotating shaft.
The method specifically comprises the following steps: establishment of epsilonxAnd εyIn a one-to-one mapping relationship
Figure BDA0002892906480000061
Using Fourier series to exiAnd εyiFitting to establish a functional relationship between the rotation angle of the rotating shaft and the tilt error motion
Figure BDA0002892906480000062
Wherein n is 7;
thereby obtaining the coordinate conversion relation of the rotating shaft
Figure BDA0002892906480000063
DiSatisfies the coordinate transformation formula T ═ Di·Treal，TrealIs a rotating shaft actual coordinate system, and T is a coordinate system after compensating the rotating shaft inclination error motion; because of ex、εyThe value is small, and a compensation formula can be obtained by simplifying the coordinate conversion relation
Figure BDA0002892906480000071
And S3, combining the compensation formula with the joint type coordinate measuring machine kinematic model, and then establishing the joint type coordinate measuring machine kinematic model containing the rotation axis inclination error motion.
The joint type coordinate measuring machine kinematic model is based on a D-H model
Figure BDA0002892906480000072
Figure BDA0002892906480000073
Wherein A isiRepresenting a homogeneous coordinate transformation matrix to determine the relative pose between adjacent rods;
combining the compensation formula with the kinematic model of the articulated coordinate measuring machine to establish the kinematic model of the articulated coordinate measuring machine containing the inclination error motion of the rotating shaft
Figure BDA0002892906480000074
The described embodiments are only some embodiments of the invention, not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

Claims (3)

1. A kinematic modeling method for an articulated coordinate measuring machine that compensates for tilt errors of a rotating shaft, comprising the steps of:
s1, building a tilt error motion test system of the rotating shaft of the articulated coordinate measuring machine, and actually measuring the tilt error motion of each rotating shaft of the articulated coordinate measuring machine;
s2, fitting the measurement result by utilizing Fourier series, and establishing a functional relation between the rotation angle of the rotating shaft and the inclination error motion so as to obtain a compensation formula of the inclination error of the rotating shaft;
and S3, combining the compensation formula with the joint type coordinate measuring machine kinematic model, and then establishing the joint type coordinate measuring machine kinematic model containing the rotation axis inclination error motion.
2. The method for modeling kinematics of an articulated coordinate measuring machine with compensation for tilt error of a rotation axis according to claim 1, wherein the calculation process of the compensation formula of S2 is specifically as follows:
establishment of epsilonxAnd εyIn a one-to-one mapping relationship
Figure FDA0002892906470000011
Using Fourier series to exiAnd εyiFitting to establish a functional relationship between the rotation angle of the rotating shaft and the tilt error motion
Figure FDA0002892906470000012
Wherein n is 7;
thereby obtaining the coordinate conversion relation of the rotating shaft
Figure FDA0002892906470000021
DiSatisfies the coordinate transformation formula T ═ Di·Treal，TrealIs a rotating shaft actual coordinate system, and T is a coordinate system after compensating the rotating shaft inclination error motion; because of ex、εyThe value is small, and a compensation formula can be obtained by simplifying the coordinate conversion relation
Figure FDA0002892906470000022
3. The method as claimed in claim 1, wherein the kinematics model of the articulated coordinate measuring machine including the tilt error of the rotation axis is S3
Figure FDA0002892906470000023
Wherein A isiAnd representing a homogeneous coordinate transformation matrix to determine the relative pose between the adjacent rods.
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